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title	weight	type
Olm & Megolm	61	docs

Olm: A Cryptographic Ratchet

An implementation of the double cryptographic ratchet described by https://whispersystems.org/docs/specifications/doubleratchet/.

Notation

This document uses \parallel to represent string concatenation. When \parallel appears on the right hand side of an = it means that the inputs are concatenated. When \parallel appears on the left hand side of an = it means that the output is split.

When this document uses \operatorname{ECDH}\left(K_A,K_B\right) it means that each party computes a Diffie-Hellman agreement using their private key and the remote party's public key. So party A computes \operatorname{ECDH}\left(K_B^{public},K_A^{private}\right) and party B computes \operatorname{ECDH}\left(K_A^{public},K_B^{private}\right).

Where this document uses \operatorname{HKDF}\left(salt,IKM,info,L\right) it refers to the HMAC-based key derivation function with a salt value of salt, input key material of IKM, context string info, and output keying material length of L bytes.

The Olm Algorithm

Initial setup

The setup takes four Curve25519 inputs: Identity keys for Alice and Bob, I_A and I_B, and one-time keys for Alice and Bob, E_A and E_B. A shared secret, S, is generated using Triple Diffie-Hellman. The initial 256 bit root key, R_0, and 256 bit chain key, C_{0,0}, are derived from the shared secret using an HMAC-based Key Derivation Function using SHA-256 as the hash function (HKDF-SHA-256) with default salt and "OLM_ROOT" as the info.


\begin{aligned}
    S&=\operatorname{ECDH}\left(I_A,E_B\right)\;\parallel\;
       \operatorname{ECDH}\left(E_A,I_B\right)\;\parallel\;
       \operatorname{ECDH}\left(E_A,E_B\right)\\
    R_0\;\parallel\;C_{0,0}&=
        \operatorname{HKDF}\left(0,S,\text{``OLM\_ROOT"},64\right)
\end{aligned}

Advancing the root key

Advancing a root key takes the previous root key, R_{i-1}, and two Curve25519 inputs: the previous ratchet key, T_{i-1}, and the current ratchet key T_i. The even ratchet keys are generated by Alice. The odd ratchet keys are generated by Bob. A shared secret is generated using Diffie-Hellman on the ratchet keys. The next root key, R_i, and chain key, C_{i,0}, are derived from the shared secret using HKDF-SHA-256 using R_{i-1} as the salt and "OLM_RATCHET" as the info.


\begin{aligned}
    R_i\;\parallel\;C_{i,0}&=
        \operatorname{HKDF}\left(
            R_{i-1},
            \operatorname{ECDH}\left(T_{i-1},T_i\right),
            \text{``OLM\_RATCHET"},
            64
        \right)
\end{aligned}

Advancing the chain key

Advancing a chain key takes the previous chain key, C_{i,j-1}. The next chain key, C_{i,j}, is the HMAC-SHA-256 of "\x02" using the previous chain key as the key.


\begin{aligned}
    C_{i,j}&=\operatorname{HMAC}\left(C_{i,j-1},\text{``\char`\\x02"}\right)
\end{aligned}

Creating a message key

Creating a message key takes the current chain key, C_{i,j}. The message key, M_{i,j}, is the HMAC-SHA-256 of "\x01" using the current chain key as the key. The message keys where i is even are used by Alice to encrypt messages. The message keys where i is odd are used by Bob to encrypt messages.


\begin{aligned}
    M_{i,j}&=\operatorname{HMAC}\left(C_{i,j},\text{``\char`\\x01"}\right)
\end{aligned}

The Olm Protocol

Creating an outbound session

Bob publishes the public parts of his identity key, I_B, and some single-use one-time keys E_B.

Alice downloads Bob's identity key, I_B, and a one-time key, E_B. She generates a new single-use key, E_A, and computes a root key, R_0, and a chain key C_{0,0}. She also generates a new ratchet key T_0.

Sending the first pre-key messages

Alice computes a message key, M_{0,j}, and a new chain key, C_{0,j+1}, using the current chain key. She replaces the current chain key with the new one.

Alice encrypts her plain-text with the message key, M_{0,j}, using an authenticated encryption scheme (see below) to get a cipher-text, X_{0,j}.

She then sends the following to Bob:

The public part of her identity key, I_A
The public part of her single-use key, E_A
The public part of Bob's single-use key, E_B
The current chain index, j
The public part of her ratchet key, T_0
The cipher-text, X_{0,j}

Alice will continue to send pre-key messages until she receives a message from Bob.

Creating an inbound session from a pre-key message

Bob receives a pre-key message as above.

Bob looks up the private part of his single-use key, E_B. He can now compute the root key, R_0, and the chain key, C_{0,0}, from I_A, E_A, I_B, and E_B.

Bob then advances the chain key j times, to compute the chain key used by the message, C_{0,j}. He now creates the message key, M_{0,j}, and attempts to decrypt the cipher-text, X_{0,j}. If the cipher-text's authentication is correct then Bob can discard the private part of his single-use one-time key, E_B.

Bob stores Alice's initial ratchet key, T_0, until he wants to send a message.

Sending normal messages

Once a message has been received from the other side, a session is considered established, and a more compact form is used.

To send a message, the user checks if they have a sender chain key, C_{i,j}. Alice uses chain keys where i is even. Bob uses chain keys where i is odd. If the chain key doesn't exist then a new ratchet key T_i is generated and a new root key R_i and chain key C_{i,0} are computed using R_{i-1}, T_{i-1} and T_i.

A message key, M_{i,j} is computed from the current chain key, C_{i,j}, and the chain key is replaced with the next chain key, C_{i,j+1}. The plain-text is encrypted with M_{i,j}, using an authenticated encryption scheme (see below) to get a cipher-text, X_{i,j}.

The user then sends the following to the recipient:

The current chain index, j
The public part of the current ratchet key, T_i
The cipher-text, X_{i,j}

Receiving messages

The user receives a message as above with the sender's current chain index, j, the sender's ratchet key, T_i, and the cipher-text, X_{i,j}.

The user checks if they have a receiver chain with the correct i by comparing the ratchet key, T_i. If the chain doesn't exist then they compute a new root key, R_i, and a new receiver chain, with chain key C_{i,0}, using R_{i-1}, T_{i-1} and T_i.

If the j of the message is less than the current chain index on the receiver then the message may only be decrypted if the receiver has stored a copy of the message key M_{i,j}. Otherwise the receiver computes the chain key, C_{i,j}. The receiver computes the message key, M_{i,j}, from the chain key and attempts to decrypt the cipher-text, X_{i,j}.

If the decryption succeeds the receiver updates the chain key for T_i with C_{i,j+1} and stores the message keys that were skipped in the process so that they can decode out of order messages. If the receiver created a new receiver chain then they discard their current sender chain so that they will create a new chain when they next send a message.

The Olm Message Format

Olm uses two types of messages. The underlying transport protocol must provide a means for recipients to distinguish between them.

Normal Messages

Olm messages start with a one byte version followed by a variable length payload followed by a fixed length message authentication code.

 +--------------+------------------------------------+-----------+
 | Version Byte | Payload Bytes                      | MAC Bytes |
 +--------------+------------------------------------+-----------+

The version byte is "\x03".

The payload consists of key-value pairs where the keys are integers and the values are integers and strings. The keys are encoded as a variable length integer tag where the 3 lowest bits indicates the type of the value: 0 for integers, 2 for strings. If the value is an integer then the tag is followed by the value encoded as a variable length integer. If the value is a string then the tag is followed by the length of the string encoded as a variable length integer followed by the string itself.

Olm uses a variable length encoding for integers. Each integer is encoded as a sequence of bytes with the high bit set followed by a byte with the high bit clear. The seven low bits of each byte store the bits of the integer. The least significant bits are stored in the first byte.

Name	Tag	Type	Meaning
Ratchet-Key	0x0A	String	The public part of the ratchet key, Ti, of the message
Chain-Index	0x10	Integer	The chain index, j, of the message
Cipher-Text	0x22	String	The cipher-text, Xi, j, of the message

The length of the MAC is determined by the authenticated encryption algorithm being used. (Olm version 1 uses HMAC-SHA-256, truncated to 8 bytes). The MAC protects all of the bytes preceding the MAC.

Pre-Key Messages

Olm pre-key messages start with a one byte version followed by a variable length payload.

 +--------------+------------------------------------+
 | Version Byte | Payload Bytes                      |
 +--------------+------------------------------------+

The version byte is "\x03".

The payload uses the same key-value format as for normal messages.

Name	Tag	Type	Meaning
One-Time-Key	0x0A	String	The public part of Bob's single-use key, Eb.
Base-Key	0x12	String	The public part of Alice's single-use key, Ea.
Identity-Key	0x1A	String	The public part of Alice's identity key, Ia.
Message	0x22	String	An embedded Olm message with its own version and MAC.

Olm Authenticated Encryption

Version 1

Version 1 of Olm uses AES-256 in CBC mode with PKCS#7 padding for encryption and HMAC-SHA-256 (truncated to 64 bits) for authentication. The 256 bit AES key, 256 bit HMAC key, and 128 bit AES IV are derived from the message key using HKDF-SHA-256 using the default salt and an info of "OLM_KEYS".


\begin{aligned}
    AES\_KEY_{i,j}\;\parallel\;HMAC\_KEY_{i,j}\;\parallel\;AES\_IV_{i,j}
    &= \operatorname{HKDF}\left(0,M_{i,j},\text{``OLM\_KEYS"},80\right)
\end{aligned}

The plain-text is encrypted with AES-256, using the key AES\_KEY_{i,j} and the IV AES\_IV_{i,j} to give the cipher-text, X_{i,j}.

Then the entire message (including the Version Byte and all Payload Bytes) are passed through HMAC-SHA-256. The first 8 bytes of the MAC are appended to the message.

Message authentication concerns

To avoid unknown key-share attacks, the application must include identifying data for the sending and receiving user in the plain-text of (at least) the pre-key messages. Such data could be a user ID, a telephone number; alternatively it could be the public part of a keypair which the relevant user has proven ownership of.

Example attacks

Alice publishes her public Curve25519 identity key, I_A. Eve publishes the same identity key, claiming it as her own. Bob downloads Eve's keys, and associates I_A with Eve. Alice sends a message to Bob; Eve intercepts it before forwarding it to Bob. Bob believes the message came from Eve rather than Alice.

This is prevented if Alice includes her user ID in the plain-text of the pre-key message, so that Bob can see that the message was sent by Alice originally.
Bob publishes his public Curve25519 identity key, I_B. Eve publishes the same identity key, claiming it as her own. Alice downloads Eve's keys, and associates I_B with Eve. Alice sends a message to Eve; Eve cannot decrypt it, but forwards it to Bob. Bob believes the Alice sent the message to him, whereas Alice intended it to go to Eve.

This is prevented by Alice including the user ID of the intended recpient (Eve) in the plain-text of the pre-key message. Bob can now tell that the message was meant for Eve rather than him.

IPR

The Olm specification (this document) is hereby placed in the public domain.

Feedback

Can be sent to olm at matrix.org.

Acknowledgements

The ratchet that Olm implements was designed by Trevor Perrin and Moxie Marlinspike - details at https://whispersystems.org/docs/specifications/doubleratchet/. Olm is an entirely new implementation written by the Matrix.org team.

Megolm group ratchet

An AES-based cryptographic ratchet intended for group communications.

Background

The Megolm ratchet is intended for encrypted messaging applications where there may be a large number of recipients of each message, thus precluding the use of peer-to-peer encryption systems such as Olm.

It also allows a recipient to decrypt received messages multiple times. For instance, in client/server applications, a copy of the ciphertext can be stored on the (untrusted) server, while the client need only store the session keys.

Overview

Each participant in a conversation uses their own outbound session for encrypting messages. A session consists of a ratchet and an Ed25519 keypair.

Secrecy is provided by the ratchet, which can be wound forwards but not backwards, and is used to derive a distinct message key for each message.

Authenticity is provided via Ed25519 signatures.

The value of the ratchet, and the public part of the Ed25519 key, are shared with other participants in the conversation via secure peer-to-peer channels. Provided that peer-to-peer channel provides authenticity of the messages to the participants and deniability of the messages to third parties, the Megolm session will inherit those properties.

The Megolm ratchet algorithm

The Megolm ratchet R_i consists of four parts, R_{i,j} for j \in {0,1,2,3}. The length of each part depends on the hash function in use (256 bits for this version of Megolm).

The ratchet is initialised with cryptographically-secure random data, and advanced as follows:


\begin{aligned}
R_{i,0} &=
  \begin{cases}
  H_0\left(R_{2^{24}(n-1),0}\right) &\text{if }\exists n | i = 2^{24}n\\
  R_{i-1,0} &\text{otherwise}
  \end{cases}\\
R_{i,1} &=
  \begin{cases}
  H_1\left(R_{2^{24}(n-1),0}\right) &\text{if }\exists n | i = 2^{24}n\\
  H_1\left(R_{2^{16}(m-1),1}\right) &\text{if }\exists m | i = 2^{16}m\\
  R_{i-1,1} &\text{otherwise}
  \end{cases}\\
R_{i,2} &=
  \begin{cases}
  H_2\left(R_{2^{24}(n-1),0}\right) &\text{if }\exists n | i = 2^{24}n\\
  H_2\left(R_{2^{16}(m-1),1}\right) &\text{if }\exists m | i = 2^{16}m\\
  H_2\left(R_{2^8(p-1),2}\right) &\text{if }\exists p | i = 2^8p\\
  R_{i-1,2} &\text{otherwise}
  \end{cases}\\
R_{i,3} &=
  \begin{cases}
  H_3\left(R_{2^{24}(n-1),0}\right) &\text{if }\exists n | i = 2^{24}n\\
  H_3\left(R_{2^{16}(m-1),1}\right) &\text{if }\exists m | i = 2^{16}m\\
  H_3\left(R_{2^8(p-1),2}\right) &\text{if }\exists p | i = 2^8p\\
  H_3\left(R_{i-1,3}\right) &\text{otherwise}
  \end{cases}
\end{aligned}

where H_0, H_1, H_2, and H_3 are different hash functions. In summary: every 2^8 iterations, R_{i,3} is reseeded from R_{i,2}. Every 2^{16} iterations, R_{i,2} and R_{i,3} are reseeded from R_{i,1}. Every 2^{24} iterations, R_{i,1}, R_{i,2} and R_{i,3} are reseeded from R_{i,0}.

The complete ratchet value, R_{i}, is hashed to generate the keys used to encrypt each message. This scheme allows the ratchet to be advanced an arbitrary amount forwards while needing at most 1020 hash computations. A client can decrypt chat history onwards from the earliest value of the ratchet it is aware of, but cannot decrypt history from before that point without reversing the hash function.

This allows a participant to share its ability to decrypt chat history with another from a point in the conversation onwards by giving a copy of the ratchet at that point in the conversation.

The Megolm protocol

Session setup

Each participant in a conversation generates their own Megolm session. A session consists of three parts:

a 32 bit counter, i.
an Ed25519 keypair, K.
a ratchet, R_i, which consists of four 256-bit values, R_{i,j} for j \in {0,1,2,3}.

The counter i is initialised to 0. A new Ed25519 keypair is generated for K. The ratchet is simply initialised with 1024 bits of cryptographically-secure random data.

A single participant may use multiple sessions over the lifetime of a conversation. The public part of K is used as an identifier to discriminate between sessions.

To allow other participants in the conversation to decrypt messages, the session data is formatted as described in Session-sharing format. It is then shared with other participants in the conversation via a secure peer-to-peer channel (such as that provided by Olm).

When the session data is received from other participants, the recipient first checks that the signature matches the public key. They then store their own copy of the counter, ratchet, and public key.

Message encryption

This version of Megolm uses AES-256 in CBC mode with PKCS#7 padding and HMAC-SHA-256 (truncated to 64 bits). The 256 bit AES key, 256 bit HMAC key, and 128 bit AES IV are derived from the megolm ratchet R_i:


\begin{aligned}
 \mathit{AES\_KEY}_{i}\;\parallel\;\mathit{HMAC\_KEY}_{i}\;\parallel\;\mathit{AES\_IV}_{i}
    &= \operatorname{HKDF}\left(0,\,R_{i},\text{"MEGOLM\_KEYS"},\,80\right) \\
\end{aligned}

where \parallel represents string splitting, and \operatorname{HKDF}\left(\mathit{salt},\,\mathit{IKM},\,\mathit{info},\,L\right) refers to the HMAC-based key derivation function using using SHA-256 as the hash function (HKDF-SHA-256) with a salt value of \mathit{salt}, input key material of \mathit{IKM}, context string \mathit{info}, and output keying material length of L bytes.

The plain-text is encrypted with AES-256, using the key \mathit{AES\_KEY}_{i} and the IV \mathit{AES\_IV}_{i} to give the cipher-text, X_{i}.

The ratchet index i, and the cipher-text X_{i}, are then packed into a message as described in Message format. Then the entire message (including the version bytes and all payload bytes) are passed through HMAC-SHA-256. The first 8 bytes of the MAC are appended to the message.

Finally, the authenticated message is signed using the Ed25519 keypair; the 64 byte signature is appended to the message.

The complete signed message, together with the public part of K (acting as a session identifier), can then be sent over an insecure channel. The message can then be authenticated and decrypted only by recipients who have received the session data.

Advancing the ratchet

After each message is encrypted, the ratchet is advanced. This is done as described in The Megolm ratchet algorithm, using the following definitions:


\begin{aligned}
    H_0(A) &\equiv \operatorname{HMAC}(A,\text{``\char`\\x00"}) \\
    H_1(A) &\equiv \operatorname{HMAC}(A,\text{``\char`\\x01"}) \\
    H_2(A) &\equiv \operatorname{HMAC}(A,\text{``\char`\\x02"}) \\
    H_3(A) &\equiv \operatorname{HMAC}(A,\text{``\char`\\x03"}) \\
\end{aligned}

where \operatorname{HMAC}(A, T) is the HMAC-SHA-256 of T, using A as the key.

For outbound sessions, the updated ratchet and counter are stored in the session.

In order to maintain the ability to decrypt conversation history, inbound sessions should store a copy of their earliest known ratchet value (unless they explicitly want to drop the ability to decrypt that history - see Partial Forward Secrecy). They may also choose to cache calculated ratchet values, but the decision of which ratchet states to cache is left to the application.

Data exchange formats

This format is used for the initial sharing of a Megolm session with other group participants who need to be able to read messages encrypted by this session.

The session sharing format is as follows:

+---+----+--------+--------+--------+--------+------+-----------+
| V | i  | R(i,0) | R(i,1) | R(i,2) | R(i,3) | Kpub | Signature |
+---+----+--------+--------+--------+--------+------+-----------+
0   1    5        37       69      101      133    165         229   bytes

The version byte, V, is "\x02".

This is followed by the ratchet index, i, which is encoded as a big-endian 32-bit integer; the ratchet values R_{i,j}; and the public part of the Ed25519 keypair K.

The data is then signed using the Ed25519 keypair, and the 64-byte signature is appended.

Session export format

Once the session is initially shared with the group participants, each participant needs to retain a copy of the session if they want to maintain their ability to decrypt messages encrypted with that session.

For forward-secrecy purposes, a participant may choose to store a ratcheted version of the session. But since the ratchet index is covered by the signature, this would invalidate the signature. So we define a similar format, called the session export format, which is identical to the session sharing format except for dropping the signature.

The Megolm session export format is thus as follows:

+---+----+--------+--------+--------+--------+------+
| V | i  | R(i,0) | R(i,1) | R(i,2) | R(i,3) | Kpub |
+---+----+--------+--------+--------+--------+------+
0   1    5        37       69      101      133    165   bytes

The version byte, V, is "\x01".

This is followed by the ratchet index, i, which is encoded as a big-endian 32-bit integer; the ratchet values R_{i,j}; and the public part of the Ed25519 keypair K.

Message format

Megolm messages consist of a one byte version, followed by a variable length payload, a fixed length message authentication code, and a fixed length signature.

+---+------------------------------------+-----------+------------------+
| V | Payload Bytes                      | MAC Bytes | Signature Bytes  |
+---+------------------------------------+-----------+------------------+
0   1                                    N          N+8                N+72   bytes

The version byte, V, is "\x03".

The payload uses a format based on the Protocol Buffers encoding. It consists of the following key-value pairs:

Name	Tag	Type	Meaning
Message-Index	0x08	Integer	The index of the ratchet, i
Cipher-Text	0x12	String	The cipher-text, Xi, of the message

Within the payload, integers are encoded using a variable length encoding. Each integer is encoded as a sequence of bytes with the high bit set followed by a byte with the high bit clear. The seven low bits of each byte store the bits of the integer. The least significant bits are stored in the first byte.

Strings are encoded as a variable-length integer followed by the string itself.

Each key-value pair is encoded as a variable-length integer giving the tag, followed by a string or variable-length integer giving the value.

The payload is followed by the MAC. The length of the MAC is determined by the authenticated encryption algorithm being used (8 bytes in this version of the protocol). The MAC protects all of the bytes preceding the MAC.

The length of the signature is determined by the signing algorithm being used (64 bytes in this version of the protocol). The signature covers all of the bytes preceding the signature.

Limitations

Message Replays

A message can be decrypted successfully multiple times. This means that an attacker can re-send a copy of an old message, and the recipient will treat it as a new message.

To mitigate this it is recommended that applications track the ratchet indices they have received and that they reject messages with a ratchet index that they have already decrypted.

Lack of Transcript Consistency

In a group conversation, there is no guarantee that all recipients have received the same messages. For example, if Alice is in a conversation with Bob and Charlie, she could send different messages to Bob and Charlie, or could send some messages to Bob but not Charlie, or vice versa.

Solving this is, in general, a hard problem, particularly in a protocol which does not guarantee in-order message delivery. For now it remains the subject of future research.

Lack of Backward Secrecy

Backward secrecy (also called 'future secrecy' or 'post-compromise security') is the property that if current private keys are compromised, an attacker cannot decrypt future messages in a given session. In other words, when looking backwards in time at a compromise which has already happened, current messages are still secret.

By itself, Megolm does not possess this property: once the key to a Megolm session is compromised, the attacker can decrypt any message that was encrypted using a key derived from the compromised or subsequent ratchet values.

In order to mitigate this, the application should ensure that Megolm sessions are not used indefinitely. Instead it should periodically start a new session, with new keys shared over a secure channel.

Partial Forward Secrecy

Forward secrecy (also called 'perfect forward secrecy') is the property that if the current private keys are compromised, an attacker cannot decrypt past messages in a given session. In other words, when looking forwards in time towards a potential future compromise, current messages will be secret.

In Megolm, each recipient maintains a record of the ratchet value which allows them to decrypt any messages sent in the session after the corresponding point in the conversation. If this value is compromised, an attacker can similarly decrypt past messages which were encrypted by a key derived from the compromised or subsequent ratchet values. This gives 'partial' forward secrecy.

To mitigate this issue, the application should offer the user the option to discard historical conversations, by winding forward any stored ratchet values, or discarding sessions altogether.

Dependency on secure channel for key exchange

The design of the Megolm ratchet relies on the availability of a secure peer-to-peer channel for the exchange of session keys. Any vulnerabilities in the underlying channel are likely to be amplified when applied to Megolm session setup.

For example, if the peer-to-peer channel is vulnerable to an unknown key-share attack, the entire Megolm session become similarly vulnerable. For example: Alice starts a group chat with Eve, and shares the session keys with Eve. Eve uses the unknown key-share attack to forward the session keys to Bob, who believes Alice is starting the session with him. Eve then forwards messages from the Megolm session to Bob, who again believes they are coming from Alice. Provided the peer-to-peer channel is not vulnerable to this attack, Bob will realise that the key-sharing message was forwarded by Eve, and can treat the Megolm session as a forgery.

A second example: if the peer-to-peer channel is vulnerable to a replay attack, this can be extended to entire Megolm sessions.

License

The Megolm specification (this document) is licensed under the Apache License, Version 2.0 http://www.apache.org/licenses/LICENSE-2.0.

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